A class of N-body problems with nearest- and next-to-nearest neighbour interactions

We obtain the exact ground state and a part of the excitation spectrum in one dimension on a line and the exact ground state on a circle in a case where N particles are interacting via nearest- and next-to-nearest neighbour interactions. Further, using the exact ground-state, we establish a mapping between these N-body problems and the short-range Dyson models introduced recently to model intermediate spectral statistics. Using this mapping we compute the one- and two-point functions of a related many-body theory and show that there is no long-range order in the thermodynamic limit. However, quite remarkably, we prove the existence of an off-diagonal long-range order in the symmetrised version of the related many-body theory. Generalisation of the models to other root systems is also considered. Besides, we also generalize the model on the full line to higher dimensions. Finally, we consider a model in two dimensions in which all the states exhibit novel correlations.Comment: LaTeX2e, 40 pages, 2 figures, submitted to Nucl. Phys. B [FS

Off-diagonal long-range order in one-dimensional many-body problem

We prove that there is off-diagonal long-range order in the symmetrised version of the one-dimensional many-body problem presented by Jain and Khare (Phys. Lett. A262 (1999)35). This model is related to the short-range Dyson model employed to study intermediate statistics in systems like the Anderson model in three dimensions at the metal-insulator transition point and pseudointegrable billiards. To the best of our knowledge, this is the only example showing quantum phases and possibility of Bose-Einstein condensation in one-dimensional statistical mechanics.Comment: LaTeX2e, submitted to Phys. Lett.

An exactly solvable many-body problem in one dimension

For N impenetrable particles in one dimension where only the nearest and next-to-nearest neighbours interact, we obtain the complete spectrum both on a line and on a circle. Further, we establish a mapping between these N-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics in some systems using which we compute the two-point correlation function and prove the absence of long-range order in the corresponding many-body theory. Further, we also show the absence of off-diagonal long-range order in these systems.Comment: LaTeX, 4 pages, 1 figur

Object Detection using Particle Swarm Optimisation and Kalman Filter to Track Partially occluded Targets

Motion estimation, object detection, and tracking have been actively pursued by researchers in the field of real time video processing. In the present work, a new algorithm is proposed to automatically detect objects using revised local binary pattern (m-LBP) for object detection. The detected object was tracked and its location estimated using the Kalman filter, whose state covariance matrix was tuned using particle swarm optimisation (PSO). PSO, being a nature inspired algorithm, is a well proven optimization technique. This algorithm was applied to important real-world problems of partially-occluded objects in infrared videos. Algorithm validation was performed by realizing a thermal imager, and this novel algorithm was implemented in it to demonstrate that the proposed algorithm is more efficient and produces better results in motion estimation for partially-occluded objects. It is also shown that track convergence is 56% faster in the PSO-Kalman algorithm than tracking with Kalman-only filter

Quantum modes on chaotic motion: analytically exact results

We discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. These results have been possible due to connections shown between random matrix models, many-body theories, and dynamical systems. We believe that these results and connections will pave the way to a better understanding of quantum chaos

Range Performance Modelling of Thermal Imaging System based on Single Parameter Characterised by Ambient Temperature and Relative Humidity

Range performance of a thermal imaging system is characterised by the prevailing atmospheric condition present at that time. There are two dominant parameters that limit the range performance of any thermal imaging systems i.e. ambient temperature and relative humidity. In the present work, comparative study of acquisition range performance of thermal imaging system operating in LWIR and MWIR spectral bands has been presented as a function of absolute humidity (AH) which is responsible for attenuation of IR radiation due to water vapour molecules present in path length. Presentation of acquisition range as function of AH leads to a single range performance table/graph for thermal imaging system under consideration for predefined visibility (V), target size, ambient temperature (T), target to background temperature difference (ΔT) and relative humidity (RH). This table/graph can be used to predict detection, recognition and identification ranges for any set of combination of air temperature (T) and relative humidity (RH). The approach presented in this paper is versatile and has been illustrated through comparative performance analysis of LWIR and MWIR thermal imaging systems based on 640X512 staring focal plane array (FPA) having identical design parameters in terms of resolution (IFOV). It has been shown that MWIR performance is superior to LWIR beyond a crossover value of AH(T) even though MRTD of MWIR sensor is inferior to that of LWIR sensor at all spatial frequencies. Study has been carried out both for clear atmosphere and hazy conditions

Performance Improvement of Electro Optic Search and Track System for Maritime Surveillance

Surveillance of maritime domain is absolutely vital to ensure an appropriate response against any adverse situation relating to maritime safety or security. Electro-optic search and track (EOST) system plays a vital role by providing independent search and track of potential targets in marine environment. EOST provides real-time images of objects with details, required to neutralise threats. At long range, detection and tracking capability of EOST degrades due to uncertainty in target signatures under cluttered scenario. Image quality can be improved by using suitable sensors and enhancement using the target/background signature knowledge. Robust tracking of object can be achieved by optimising the performance parameters of tracker. In the present work, improvement in the performance of EOST subsystems such as sensor, video processor and video tracker are discussed. To improve EOST performance in terms of detection and tracking, sensor selection criterion and various real time image processing techniques and their selection criteria for maritime applications have been also discussed. Resultant improvement in the quality of image recorded under marine environment has been presented

Real Time Non uniformity Correction Algorithm and Implementation in Reconfigurable Architecture for Infra red Imaging Systems

 In modern electro-optical systems, infra-red (IR) imaging system is an essential sensor used for day and night surveillance. In recent years, advancements in IR sensor technology resulted the detectors having smaller pitch, better thermal sensitivity with large format like 640.512, 1024.768 and 1280.1024. Large format IR detectors enables realisation of high resolution compact thermal imager having wide field-of view coverage. However, the performance of these infrared imaging systems gets limited by non uniformity produced by sensing element, which is temporal in nature and present in spatial domain. This non uniformity results the fixed pattern noise, which arises due to variation in gain and offset components of the each pixel of the sensor even when exposed to a uniform scene. This fixed pattern noise limits the temperature resolution capability of the IR imaging system thereby causing the degradation in system performance. Therefore, it is necessary to correct the non-uniformities in real time. In this paper, non uniformity correction algorithm and its implementation in reconfigurable architectures have been presented and results on real time data have been described

Thermal (Infrared) Imaging Sensors (Review Paper)

Recent developments in improved type of infrared detector technologies focal plane arrays,signal processing techniques, and innovative optical designs have enabled thermal imagingtechnology to undergo revolutionary advancement, leading to realisation of high performanceand compact thermal cameras for surveillance, target acquisition, tracking, and guidance.Instruments Research and Development Establishment (IRDE), Dehradun, has designed anddeveloped a variety of thermal imaging sights for different ongoing programmes/projects. In thepresent paper, an overview of thermal imaging systems, different generations and classificationof thermal imaging systems is described. The paper also presents salient features/specificationsof thermal imaging systems developed by IRDE together with the images recorded in actual fieldtrials